Unfortunately gaming laptops do not get 5+ hours of battery life. The good news is that your budget does allow for a really good option. With that said, I suggest to you the
MSI GT60 Dominator-424 with:
i7-4800MQ
8GB RAM
1TB 7200RPM HDD
Nvidia GTX 870M Graphics
15.6" 1920x1080 Display
Custom Backlit Keyboard by Steelseries
Dynaudio Premium Sound w/ Subwoofer
Killer Doubleshot Networking
It's the most powerful gaming option given the budget, however it isn't really thin. A much thinner option (1.1in), although not nearly as powerful (but still well capable) is the
ASUS N550JK with:
i7-4700MQ
8GB RAM
1TB 5400RPM HDD
Nvidia GTX 850M Graphics
Beautiful 15.6" 1920x1080 IPS Touch Display
You may actually be able to squeeze 5 hours of battery life out of this one.